# Thread: Polynomial Expansion Using Pascals Triangle

1. ## Polynomial Expansion Using Pascals Triangle

Heres the question followed by the textbook answer from the back.

Im stuck on how it got the answer. Ive just done about 5 others in the same way, but this one doesn't seem to give me the right answer.

I got:

$\displaystyle 1+12x+30x^2+40x^3+30x^4+12x^5+2x^6$

I did the correct method i think.
Heres the row of the pascal triangle i used:

1 6 15 20 15 6 1

So i basicly did:

$\displaystyle (1)(1^6)(2x^0) + (6)(1^5)(2x^1) + (15)(1^4)(2x^2)$... etc and simplified. I really don't understand how i got the answer wrong. Any suggestions?

2. Hello,

Originally Posted by nugiboy
Heres the question followed by the textbook answer from the back.

Im stuck on how it got the answer. Ive just done about 5 others in the same way, but this one doesn't seem to give me the right answer.

I got:

$\displaystyle 1+12x+30x^2+40x^3+30x^4+12x^5+2x^6$

I did the correct method i think.
Heres the row of the pascal triangle i used:

1 6 15 20 15 6 1

So i basicly did:

$\displaystyle (1)(1^6)({\color{red}(}2x{\color{red})}^0) + (6)(1^5)({\color{red}(}2x{\color{red})}^1) + (15)(1^4)({\color{red}(}2x{\color{red})}^2)$... etc and simplified. I really don't understand how i got the answer wrong. Any suggestions?
The mistakes are in red

3. Remember that it is $\displaystyle \left(1+\left(2x\right)\right)^6$!